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Mirrors > Home > NFE Home > Th. List > ssofeq | Unicode version |
Description: When and are subsets of , equality depends only on the elements of . (Contributed by SF, 13-Jan-2015.) |
Ref | Expression |
---|---|
ssofeq |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssofss 4076 | . . 3 | |
2 | ssofss 4076 | . . 3 | |
3 | 1, 2 | bi2anan9 843 | . 2 |
4 | eqss 3287 | . 2 | |
5 | ralbiim 2751 | . 2 | |
6 | 3, 4, 5 | 3bitr4g 279 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wb 176 wa 358 wceq 1642 wcel 1710 wral 2614 wss 3257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ral 2619 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-un 3214 df-ss 3259 |
This theorem is referenced by: eqpw1 4162 pw111 4170 eqrelk 4212 sikexlem 4295 insklem 4304 |
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